Axially compliant bearing for precision positioning

ABSTRACT

A rotationally compliant bearing roller assembly having a roller, at least one bearing member operably coupled to a base configured to support rotational movement about a rotational axis; and a rotary compliant joint interconnecting the at least one bearing member to the roller. The rotary compliant joint having a first compliance in a rotational direction about the rotational axis to permit movement of the roller in the rotational direction relative to the at least one bearing member, such that the first compliance being greater than a friction induced compliance of the at least one bearing member in the rotational direction. The compliant joint having a second compliance in a direction orthogonal to the rotational direction, such that the second compliance being less than the first compliance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 15/772,952 filed on May 2, 2018, which is a National Stage ofInternational Application No. PCT/US2016/060033 filed on Nov. 2, 2016,which claims the benefit of U.S. Provisional Application No. 62/249,589,filed on Nov. 2, 2015. The entire disclosure of the above applicationsare incorporated herein by reference.

FIELD

The present disclosure relates to a motion system and, moreparticularly, relates to a motion stage equipped with an axiallycompliant rolling bearing and/or a rotary system equipped with a rotarycompliant system.

BACKGROUND AND SUMMARY

This section provides background information related to the presentdisclosure which is not necessarily prior art. This section provides ageneral summary of the disclosure, and is not a comprehensive disclosureof its full scope or all of its features.

Precision motion stages are designed for precise positioning in variousmanufacturing processes. Among the bearing options for precision stages,rolling bearings are the most cost effective, especially forapplications requiring large motion range and vacuum compatibility.However, the presence of nonlinear friction adversely affects theprecision and speed of rolling bearing guided stages. The state of artin addressing this problem is to perform model-based frictioncompensation, which suffer from robustness problems, thus limiting theirusefulness in practice. This invention addresses the problem ofnonlinear effect of friction in rolling bearing guided stages by usingcompliant joint(s) to provide a simple, model-free and potentiallylow-cost approach.

In some embodiments according to the principles of the presentteachings, a precision motion stage equipped with an axially compliantroller bearing is provided having a stage, at least one bearing slidablydisposed along a rail, and a compliant joint interconnecting the atleast one bearing to the stage. The compliant joint is sufficientlycompliant to permit movement of the stage in the desired motiondirection (i.e., axial direction) while remaining stiff in otherorthogonal directions to maintain the high rigidity of the bearings.

Similarly, high precision roll-to-roll processes are one of the mostpromising technologies for manufacturing flexible and large-area thinfilm electronics. However, broadband frictional disturbances caused bythe guiding ball bearings affect the precision of the processing roller116 in the roll-to-roll system, severely hampering the quality of themanufactured products. Conventional feedback control techniquesencounter difficulties in mitigating the broadband frictionaldisturbances.

In some embodiments according to the principles of the presentteachings, a rotary system for high-precision roll-to-roll manufacturingprocess is provided. A rotary compliant joint, being a robust andcost-effective mechatronics system, is implemented in the roll-to-rollmanufacturing system to mitigate the undesirable effects of frictionduring continuous printing processes. Frequency domain analysis showsthat the rotary system with one or more rotary compliant joints achievessignificantly improved attenuation of frictional disturbance, comparedto the case without it. In some embodiments, a rotary compliant joint isdesigned and optimized to minimize the adverse effects of bearingfriction without overly sacrificing the high rigidity of the machine. Ithas been demonstrated that the present teachings provide up to 61%reduction in root mean square (RMS) tracking error during constantvelocity motion, compared to a conventional roll-to-roll system withoutone or more rotary compliant joints.

Further areas of applicability will become apparent from the descriptionprovided herein. The description and specific examples in this summaryare intended for purposes of illustration only and are not intended tolimit the scope of the present disclosure.

DRAWINGS

The drawings described herein are for illustrative purposes only ofselected embodiments and not all possible implementations, and are notintended to limit the scope of the present disclosure.

FIG. 1 is a schematic view of an axially compliant rolling bearingprecision motion stage according to the principles of the presentteachings;

FIG. 2(a) is a three-mass model of the axially compliant rolling bearingstage according to the principles of the present teachings;

FIG. 2(b) is a three-mass model of a rolling bearing stage according tothe prior art;

FIG. 3(a) is a graph illustrating the settling time of the axiallycompliant rolling bearing stage and the regular rolling bearing stage inresponse to a 100 nm step command;

FIG. 3(b) is a graph illustrating the effect of compliant jointstiffness on settling time of the axially compliant rolling bearingstage;

FIG. 4(a) is a graph illustrating position versus time of a typicalsinusoidal displacement profile;

FIG. 4(b) is a graph illustrating the tracking error of the axiallycompliant rolling bearing stage with different compliant jointstiffness;

FIG. 5 is a graph illustrating the effect of compliant joint stiffnesson peak and root-mean-square (RMS) tracking errors of the axiallycompliant rolling bearing stage;

FIG. 6 is a schematic view illustrating a negative stiffness mechanismusing beam buckling;

FIG. 7(a) is a schematic view illustrating a negative stiffnessmechanism using attraction force between a pair of permanent magnets;

FIG. 7(b) is a schematic view illustrating a negative stiffnessmechanism using repulsion force between a pair of permanent magnets;

FIG. 8 is a schematic view of compliant joint design I according to theprinciples of the present teachings;

FIG. 9 is an exploded perspective view of compliant joint design Iaccording to the principles of the present teachings.

FIG. 10 is a perspective view of an axially compliant rolling bearingstage according to the principles of the present teachings;

FIG. 11 is a schematic view of compliant joint design II according tothe principles of the present teachings;

FIG. 12 is a schematic view of a coarse-fine stage according to theprior art; and

FIG. 13 is a schematic view of an axially compliant rolling bearingprecision motion stage according to the principles of the presentteachings;

FIG. 14 is a schematic view of an rotationally compliant bearing rollerassembly according to the principles of the present teachings;

FIG. 15A is a schematic perspective view of a conventional rotary systemfor roll-to-roll manufacturing;

FIG. 15B is a schematic perspective view of a rotary system forroll-to-roll manufacturing having a rotary compliant joint according tothe principles of the present teachings;

FIG. 16 is a schematic view of a control system for controlling therotationally compliant bearing roller assembly of the present teachings;

FIGS. 17A and 17B are frequency versus magnitude graphs for differentstiffness k; for configurations without and with rotary compliantjoints, respectively;

FIG. 18A is a perspective view of a compliant joint rotary systemaccording to the principles of the present teachings;

FIG. 18B is an enlarge cross-sectional view of the compliant jointrotary system according to the principles of the present teachings;

FIGS. 19A and 19B are a side and perspective view of a rotary compliantjoint, in the form of a symmetric cartwheel flexure mechanism, accordingto the principles of the present teachings; and

FIG. 20 illustrates the calculated stiffness ratio of K₁₁ (and K₂₂) overK₆₆ as a function of α and l.

Corresponding reference numerals indicate corresponding parts throughoutthe several views of the drawings.

DETAILED DESCRIPTION

Example embodiments will now be described more fully with reference tothe accompanying drawings.

Example embodiments are provided so that this disclosure will bethorough, and will fully convey the scope to those who are skilled inthe art. Numerous specific details are set forth such as examples ofspecific components, devices, and methods, to provide a thoroughunderstanding of embodiments of the present disclosure. It will beapparent to those skilled in the art that specific details need not beemployed, that example embodiments may be embodied in many differentforms and that neither should be construed to limit the scope of thedisclosure. In some example embodiments, well-known processes,well-known device structures, and well-known technologies are notdescribed in detail.

The terminology used herein is for the purpose of describing particularexample embodiments only and is not intended to be limiting. As usedherein, the singular forms “a,” “an,” and “the” may be intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. The terms “comprises,” “comprising,” “including,” and“having,” are inclusive and therefore specify the presence of statedfeatures, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof. The method steps, processes, and operations described hereinare not to be construed as necessarily requiring their performance inthe particular order discussed or illustrated, unless specificallyidentified as an order of performance. It is also to be understood thatadditional or alternative steps may be employed.

When an element or layer is referred to as being “on,” “engaged to,”“connected to,” or “coupled to” another element or layer, it may bedirectly on, engaged, connected or coupled to the other element orlayer, or intervening elements or layers may be present. In contrast,when an element is referred to as being “directly on,” “directly engagedto,” “directly connected to,” or “directly coupled to” another elementor layer, there may be no intervening elements or layers present. Otherwords used to describe the relationship between elements should beinterpreted in a like fashion (e.g., “between” versus “directlybetween,” “adjacent” versus “directly adjacent,” etc.). As used herein,the term “and/or” includes any and all combinations of one or more ofthe associated listed items.

Although the terms first, second, third, etc. may be used herein todescribe various elements, components, regions, layers and/or sections,these elements, components, regions, layers and/or sections should notbe limited by these terms. These terms may be only used to distinguishone element, component, region, layer or section from another region,layer or section. Terms such as “first,” “second,” and other numericalterms when used herein do not imply a sequence or order unless clearlyindicated by the context. Thus, a first element, component, region,layer or section discussed below could be termed a second element,component, region, layer or section without departing from the teachingsof the example embodiments.

Spatially relative terms, such as “inner,” “outer,” “beneath,” “below,”“lower,” “above,” “upper,” and the like, may be used herein for ease ofdescription to describe one element or feature's relationship to anotherelement(s) or feature(s) as illustrated in the figures. Spatiallyrelative terms may be intended to encompass different orientations ofthe device in use or operation in addition to the orientation depictedin the figures. For example, if the device in the figures is turnedover, elements described as “below” or “beneath” other elements orfeatures would then be oriented “above” the other elements or features.Thus, the example term “below” can encompass both an orientation ofabove and below. The device may be otherwise oriented (rotated 90degrees or at other orientations) and the spatially relative descriptorsused herein interpreted accordingly.

Introduction and Motivation

Precision motion stages are used for precise positioning inmanufacturing processes, ranging from conventional machining tosemiconductor fabrication and inspection. Precision stages can beclassified into four broad categories based on the type of bearings theyuse:

Flexure bearings

Magnetic levitation (maglev) bearings

Fluidic bearings (hydrostatic and aerostatic)

Mechanical bearings

It should be understood that mechanical bearings can include bothrolling and sliding bearings. Generally, rolling bearings are morecommon. In the interest of discussion, rolling bearing will be describedin detail herein. However, this should not be regarded as limiting thescope of the present disclosure and claim, unless specifically claimedas such.

Flexure bearings are friction free and vacuum/cleanroom compatible, butare suitable only for short-stroke motion (<1 mm) applications, whichare not of interest to this invention. For long-stroke applications (>25mm), the choice is generally between maglev, fluidic, and rollingbearings.

Maglev stages are essentially friction free, but are very expensive.They are used only in the highest end, multi-million dollar stages,e.g., wafer scanners for photolithography (made by companies like ASMLHoldings, Ultratek Inc., Nikon). They have not gained widespreadcommercial acceptance for most other applications of precision stagesdue to their cost barrier and complexities.

Fluidic bearings can either be hydrostatic or aerostatic. Hydrostaticbearings employ pressurized oil while aerostatic bearings use a thinfilm of pressurized air to reduce the friction between sliding surfaces.Hydrostatic bearings provide reduced friction and excellent dampingcharacteristics but are unsuitable for cleanroom environments, where alot of precision stages are used, because oil can easily createcontaminants. Aerostatic (or air) bearings have a minimal amount offriction. They are also cleanroom-compatible and are relatively muchcheaper than maglev bearing stages. However, they are not vacuumcompatible, which makes them unsuitable for the growing number ofapplications of precision stages that must be performed in ultrahighvacuum (UHV), e.g., electron microscopy, thin-film sputtering andfocused ion beam. Moreover, they suffer from in-position stabilityissues due to the jitter (aka ‘air hammering’) generated by the airflowthrough the bearings.

Rolling bearings are the most cost-effective of the various options.They can provide accuracies comparable to air bearing stages for motionranges less than 300 mm and they have excellent in-position stability.When lubricated with small amounts of grease, they do not create anysignificant contamination in cleanroom environments. Examples ofcommercial rolling-bearing-based motion stages include the ANT Seriesfrom Aerotech Inc. and the XM Series from Newport Corporation. They arevery attractive as a lower cost alternative to air bearing stages for awide range of precision positioning applications, and are currently theonly viable alternative to maglev bearings for applications that requirevacuum-compatibility. However, the presence of nonlinear frictionadversely affects the stage precision and speed in both the macro-(i.e., sliding) and micro-displacement (i.e., pre-sliding) regimes offriction.

In the sliding regime, friction can be characterized by the Stribeckcurve, consisting of static, Coulomb and viscous friction. Stick-slip isa common phenomenon that occurs due to the highly nonlinear behavior atvelocity reversals. Its effect is often noticeable as spikes (glitches)at quadrant locations when generating circular motions using a motionstage. On the other hand, in the pre-sliding regime, friction behaves asa nonlinear spring due to elastic deformations between rolling/slidingelements. This becomes dominant as the stage gets within microns of itsdesired position, resulting 5-10 times longer settling time thanequivalent frictionless stages in point-to-point positioning. Such longsettling times severely hamper the throughput of the processes for whichrolling bearing guided stages are used.

STATE OF THE ART

Avoidance and compensation are the two primary ways of mitigating thenonlinear effects of friction. For example, nonlinear friction can beavoided via bearing/lubricant selection and reduction of the number ofrubbing mechanical elements. When friction cannot be completely avoided,further reduction of its adverse effects can be achieved by model-freeand/or model-based compensation techniques.

Model-free approaches make use of high gain feedback control (e.g.,stiff PD or high integral gain) to increase disturbance rejection, butthey make the systems prone to instability due to sensor noise andmodeling errors. Model-based techniques generate compensatory controlforces using approximate models of friction, through feed forward orfeedback controllers.

In feed forward friction compensation (FF-FC), a prediction of theimpending frictional force is made using a model of the frictionalbehavior of the stage combined with the reference velocity of the stage.The predicted frictional force is then injected into the control inputof the stage to pre-emptively cancel out the actual friction of thestage. FF-FC works very well if the friction model is very accurate.However, the problem is that friction, particularly at the pre-slidingregime, is very temperamental and difficult to model accurately.Therefore, FF-FC methods suffer from poor robustness which could easilydegrade their performance. Model parameter adaptation has been tried asa solution to this problem but convergence of adaptation schemes isoften difficult and slow because the identification signals are oftennot rich (or persistent) enough. Another major problem with FF-FCmethods is that they depend on the reference velocity to predictfriction. When the stage is trying to settle to a desired position, thereference velocity is zero, even though the actual velocity is not.Therefore, even if the friction model is accurate, the disparity betweenthe reference and actual velocities hampers the performance of FF-FCmethods when it comes to improving settling performance.

In feedback friction compensation (FB-FC), the actual states (e.g.,velocity, position) of the system are utilized (alongside the referencestates) to predict and cancel out the force of friction. This alleviatesthe problem related to having a stagnant velocity command duringsettling in FF-FC schemes. However, the use of feedback coulddestabilize the control system for the precision stage.

Feedback friction compensation approaches make use of actual states(e.g., position and velocity) of the system to improve disturbancerejection, using gain scheduling controllers, friction observers, etc.FB-FC methods that employ a model of friction (e.g., observer-basedmethods, gain scheduling controllers, etc.) suffer from robustnessissues due to the variability of friction. Several methods have beenproposed in the literature for improving the robustness of model-basedfriction compensation methods through model parameter adaptation.However, the convergence of adaptation schemes is often unreliable andslow because the identification signals are not rich (or persistentenough).

Concepts of Axially Compliant Rolling Bearing Stage

The present teachings propose a simple, model-free approach to mitigatenonlinear effect of friction in rolling bearing guided stages by the useof axially compliant joints. As illustrated in FIG. 1, an axiallycompliant bearing stage assembly 10 is provided having a stage member 12is coupled to one or more bearing members 14 (e.g. mechanical bearingmembers such as rolling bearings and/or sliding bearings) via one ormore compliant joints 16. Bearing members 14 are coupled to a rail 18for movement relative thereto, such as rolling and/or sliding movement.In some embodiments, as illustrated, axially compliant bearing stageassembly 10 comprises stage member 12 being coupled to a plurality ofbearing members 14 via compliant joint 16 disposed at each connectinginterface. In some embodiments, axially compliant bearing stage assembly10 can comprise the following features:

P-1) Each bearing member 14 is not rigidly connected to stage member 12,but is attached using a compliant joint 16 (e.g., flexure).

P-2) Compliant joint 16 provides sufficient compliance in motiondirection of stage member 12 (i.e., axial direction) while remainingstiff in other orthogonal directions (i.e., horizontal and vertical).The combined stiffness of compliant joint 16 and the bearing member 14is in the same order of magnitude as the stiffness of the bearing member14 alone in directions orthogonal to the axial direction.

P-3) Compliant joint 16 behaves as a low pass filter which attenuatesthe frictional nonlinearity and hysteresis in both pre-sliding andsliding regimes.

Additional features can be used to optimize the performance of axiallycompliant bearing stage assembly 10 and make it more “intelligent”, suchas:

P-4) The damping coefficient of compliant joint 16 can be increased byattaching free and/or constrained damping layers, and/or by activedamping control through the actuation force 20 of stage member 12.

P-5) An intelligent supervisory controller 22 can be used to compensatefor the stiffness of compliant joint 16 in order to optimize theperformance of axially compliant bearing stage assembly 10. In someembodiments, intelligent supervisory controller 22 can use estimation ormeasurement of bearing states to apply compensatory force. In someembodiments, intelligent supervisory controller 22 can use the knowledgeof measured stage 12 position, compliant joint stiffness, combined withestimated or measured bearing 14 position to apply the compensationforce in a feed forward or feedback manner.

P-6) Smart materials, such as magnetorheological or electrorheologicalfluids, can be added to tune the stiffness and damping of compliantjoint 16 as a function of stage member 12 operation. For instance, thestiffness of compliant joint 16 can remain low during the low speedand/or small distance movements. This way, an actuator 24 exertingactuation force 20 on stage member 12 does not need to provide a largeamount of force to position stage member 12. During the high speedand/or large distance movements, compliant joint 16 stiffness can beincreased to mitigate negative effects arising from excessive vibrationscaused by sprung masses of compliant joint 16 and bearing member 14.

P-7) Similar benefits can be achieved by adopting a progressivestiffness approach when designing the compliant components (e.g.compliant joint 16). The stiffness remains low when the displacement issmall which mitigates the problematic pre-sliding friction. When largemotions are experienced, the flexure (e.g. compliant joint 16) becomesvery stiff and behaves likes a rigid connection between stage member 12and bearing members 14. These additional features create a semi-activeflexure mechanism, improving the performance and robustness.

P-8) Alternatively, engaging/disengaging mechanisms 26 can be added tolock compliant joint 16, thus converting compliant joint 16 into a morerigid block. During the high speed and/or large motions, the bearings 14behave more like regular bearing members and the negative effect fromoscillation of the sprung masses is mitigated.

In general, without compliant joints 16, bearing members 14 will get“stuck” when they encounter nonlinear friction in the pre-slidingregime, thereby directly affecting the precision and speed of axiallycompliant bearing stage assembly 10. However, with the added compliantjoints 16, even when the bearing members 14 get stuck due to friction,compliant joints 16 allow stage member 12 to make small movements (μm tomm level) thus minimizing (or isolating) the effect of nonlinearfriction from stage member 12. As a result, axially compliant bearingstage assembly 10 is able to achieve large-range, high-payload precisepositioning with one sensor and one actuator, thus significantlyreducing its cost compared to coarse-fine stage according to the priorart.

Note that, even though axially compliant bearing stage assembly 10 isdepicted using a stage with one rail 18 and two bearings 14 in FIG. 1,it is applicable to other stage configurations (e.g., a stage with tworails 18 and four bearings 14, or other variations).

Simulation Based Analysis of Compliant Augmented Stage

FIG. 2(a) shows a simple three-mass model of axially compliant bearingstage assembly 10 (closed-loop controlled through actuation forceF_(a)). Each compliant joint 16 connecting stage member 12 of mass m_(s)to each bearing 14 of mass m_(b) is modeled by a spring with stiffness kand a damper with coefficient c. Friction force F_(f), is described bythe LuGre model given by

$\begin{matrix}{{{F_{f} = {{\sigma_{0}z} + {\sigma_{1}\overset{.}{z}} + {\sigma_{2}\overset{.}{x}}}};}{{\overset{.}{z} = {\overset{.}{x} - {\frac{\overset{.}{x}}{g\left( \overset{.}{x} \right)}z}}};}{{\sigma_{0}{g\left( \overset{.}{x} \right)}} = {F_{c} + {\left( {F_{s} - F_{c}} \right)e^{- {({\overset{.}{x}/v_{s}})}^{2}}}}}} & (1)\end{matrix}$

where x represents the displacement between the two surfaces in relativemotion, z is the internal friction state, σ₀ is the micro-stiffness,while σ₁ and σ₂ are respectively the micro- and macro-dampingcoefficients. The steady-state dynamics, g({dot over (x)}), ischaracterized by the Stribeck curve with Coulomb friction F_(c), staticfriction F_(s) and the Stribeck velocity v_(s).

Axially compliant bearing stage assembly 10 is evaluated using two casestudies related to pre-sliding and sliding regimes, respectively,namely, settling behavior in point-to-point motion and trackingperformance in circular motion. Simulations are carried out based onidentified parameters of an in-house built precision motion stage by theinventors.

FIG. 3(a) shows the settling behavior of axially compliant bearing stageassembly 10 to a 100 nm step command; ±10 nm is used as the settlingwindow. As shown in FIG. 2(b), the baseline stage model has rigidconnections between stage member 12 and bearing members 14. Augmentingthe baseline stage, which only has bearing members 14 for guidance, withcompliant joints 16 (k=10⁵ N/m, c=238 N·s/m) achieves about 50%reduction in settling time. FIG. 3(b) shows the settling time as afunction of the joint stiffness (with 3% damping ratio). When the jointstiffness is high, the addition of compliance provides negligiblebenefit, but with k below a critical stiffness, which is related to themicro-stiffness of the LuGre model, a significant reduction in settlingtime is achieved.

FIG. 4 shows the simulated tracking performance of axially compliantbearing stage assembly 10, subjected to a sinusoidal reference signalwith 0.5 mm amplitude and 1 mm/s maximum velocity. The baseline stagesuffers from large quadrant glitches (error spikes) at velocityreversals with tracking errors reaching 1.6 μm. With compliant joints 16of k=10⁵ N/m and c=238 N·s/m, the augmented stage achieves 43% and 22%reductions in the peak and RMS tracking errors, respectively. If thecompliance is further reduced to k=10³ N/m, the peak and RMS errors arereduced by 98% and 95%, respectively. As shown in FIG. 5, the effect ofreduced joint stiffness on reducing quadrant glitches is in agreementwith the reduced settling time of point-to-point motions, indicating thepresent approach is able to mitigate nonlinear friction in bothpre-sliding and sliding regimes.

The analysis also implies that performance of axially compliant bearingstage assembly 10 increases monotonically as the joint stiffness in themoving direction reduces for both case studies. As the stiffnessreduces, the low-pass filtering effect of compliant joint 16 improves(i.e., equivalent cut-off frequency reduces), leading to betterattenuation of the frictional nonlinearity.

Design of Compliant Joint

Flexure mechanism could be applied to the proposed augmented rollingbearing stage (as compliant joint 16) without the need for additionalactuator and sensor. The role of compliant joint 16 is to provide somecompliance between stage member 12 and bearing member 14; thus, theadditional load of the substrate does not significantly affect thepositioning performance of axially compliant bearing stage assembly 10.Since compliant joint 16 and bearing member 14 are arranged in series,the vertical and horizontal stiffness of compliant joint 16 inorthogonal directions have to be much larger than its axial stiffness(i.e., stiffness in the moving direction) such that the combinedstructure has stiffness with same order of magnitude as those of thebearing member 14 alone (i.e., high rigidity of bearing member 14 is notsacrificed). As the stiffness of compliant joint 16 in three directionsare all coupled, there is clearly a tradeoff between achieving highperformance in mitigating nonlinear friction (i.e., low axial stiffness)and maintaining good rigidity of bearing member 14 (high stiffness inother orthogonal directions).

A potential way of achieving very low axial stiffness is to use a hybridjoint design that combines a flexure mechanism (positive stiffness) inparallel with a negative stiffness mechanism. The idea is to designcompliant joint 16 using flexure to achieve minimum axial stiffnesswhile remaining stiff in orthogonal directions. The negative stiffnessis implemented in parallel with the flexure such that the stiffness inmotion direction is further reduced. Two commonly used methods toachieve negative stiffness are considered, namely a bi-stable buckledbeam and permanent magnets (PMs).

A simple negative stiffness structure can be created from apre-compressed beam. As shown in FIG. 6, the beam is pre-loaded by ahorizontal force F_(cr) of magnitude greater than the critical force forthe first buckling mode predicted by the Euler beam model. When anotherforce F is applied in the motion direction, due to the buckling effect,the beam is switched from one stable state to the other (this is knownas the snap-through phenomenon). The equivalent stiffness during thisprocess is negative, which can be demonstrated both analytically andexperimentally. It is suggested that if higher magnitude negativestiffness is required, large preload force has to be applied to thebeam. This makes axially compliant bearing stage assembly 10 prone tostructural failure or instability as a result of higher order bucklingmodes.

Another approach to provide the negative stiffness is through the use ofpermanent magnets. As shown in FIG. 7(a), a pair of equally-sizedpermanent magnets (PMs) 40, 42 is placed on two sides of a stage member44 (made of ferrous material). If the distance between each PM 40, 42and stage member 44 is equal (i.e., d₁=d₂), attraction forces on twosides perfectly cancel out, resulting zero net force at stage member 44.Now consider the case when stage member 44 moves slightly towards left(i.e., d₁>d₂), then the attraction force from the left side (i.e.,between PM2 42 and stage 44) becomes larger than the force from theright side (i.e., between PM1 40 and stage 44); thus the net force movesstage member 44 further to the left. The magnitude of the equivalentnegative stiffness becomes larger as the difference between two gapsbecomes larger. Because of this increasing negative stiffness, thepositive stiffness of the flexure has to be designed larger than themaximum negative stiffness achieved from the pair of permanent magnetsto prevent collision.

An alternative way is to make use of the repulsion forces instead (seeFIG. 7(b)); note that the polarities of PM1 40 and PM2 42 are arrangedin opposite directions as indicated by the arrows. When the twopermanent magnets 40, 42 are perfectly aligned (d=0), the system is atan equilibrium state, as there is no force in the horizontal direction(or moving direction). Again, assume stage member 44 moves slightly tothe left, a repulsion force is generated which pushes stage member 44further to the left. The magnitude of the negative stiffness of thisembodiment is reduced as the gap between the two permanent magnetsincreases. Note that PM arrays, such as alternating polarity array andHalbach array, can be used in both arrangements to provide higher forcedensities.

Axially Compliant Bearing Design I

FIG. 8 shows the side view of a possible design of compliant joint 16which combines a flexure mechanism 46 with a pair of permanent magnets40, 42 (using the approach described in FIG. 7(b)). The flexure 46 isdesigned with a vertical leaf spring structure because of its highstiffness ratio between orthogonal directions and motion direction.Stage member 12 is mounted on the center platform where PM 40 isattached at the bottom. The bearing member 14 is mounted to the outerplatform 48 where another PM 42 is attached to provide the negativestiffness in horizontal direction. The magnitude of it is comparable tothe flexure 46 stiffness such that the combined structure hasapproximately zero stiffness when the relative motion between thebearing member 14 and stage 12 is small. Notice that the influence ofeffective stiffness of the PM pair in the other two directions isnegligible because they are significantly smaller than the stiffness offlexure in those directions.

FIG. 9 shows the detailed CAD drawing of proposed design I usingSolidWorks®. Notice that small permanent magnets are arranged withalternating polarities to form the top and bottom arrays in order toincrease the magnetic field strength. FIG. 10 shows the implementationof actual manufactured compliant joints 16 on an in-house builtprecision motion stages. Table 1 summarizes the simulated stiffnessvalues of the flexure, PM pair, bearing member 14 and combinedstructure. Notice that the combined stiffness of compliant joint 16 andbearing member 14 in the vertical and horizontal directions have thesame order of magnitude as those of the bearing member 14 alone,implying that the high stiffness of the bearing is not sacrificed.

TABLE 1 Stiffness values of the flexure, bearing member 14, permanentmagnets and their combination [N/μm] Axial Vertical Horizontal Bearingmember 14 N/A 175 58 Flexure 46 0.17 195 85 permanent magnets −0.15 0.21−0.006 Combined 0.02 92 34

Axially Compliant Bearing Design II

FIG. 11 shows the top view of an alternative design of compliant joint16 which combines the flexure mechanism 46 with two pairs of permanentmagnets 50, 52. The bearing member 14 is connected to the outer platformof compliant joint 16 and stage member 12 is attached to the centralplatform. Symmetric horizontal leaf springs are used to provide thepositive stiffness such that the parasitic motions in the horizontal andvertical directions are minimized.

Comparisons between Coarse-fine Stage and Axially Compliant RollingBearing Stage Assembly

To achieve low-cost precision positioning with large motion range, aso-called ‘coarse-fine’ stage is typically used to mitigate frictionphenomenon (it is typically commercially from companies like Newport,PI, Aerotech, etc. FIG. 12 shows the concept of coarse-fine stage whichcombines rolling bearings and flexure bearings. The rolling bearings areused to generate large-range coarse motion while the flexure bearingsare used to create short-range fine (or precise) motion. In coarse-finestage arrangements, both coarse and fine stages need to be controlled.Thus, at least two actuators and two sensors are needed. On one hand,one long-range actuator (e.g., linear motor or ball screw) drives therolling bearing coarse stage and a sensor (e.g., linear encoder) is usedto measure the coarse stage displacement. On the other hand, ashort-range actuator (e.g., voice coil or piezo actuator) drives thefine stage whose displacement is measured by a high-resolution sensor(e.g., capacitive probe, laser interferometer). Because coarse-finestage makes use of two bearings, two actuators and two sensors, they arebulky and relatively expensive. In the meantime, in order to coordinatecoarse and fine stages for optimal positioning performance, complicatedcontrollers or trajectory generation schemes are usually required. Thecoarse-fine stage also has limited load capacities because mass of finestage and power of fine actuator is usually small and weak due to thelimited space. The dynamics of the fine stage can be adversely affectedby heavy loads from the substrate placed on it.

As shown in FIG. 13, in some embodiments, axially compliant bearingstage assembly 10 makes use of compliant joint 16 (e.g., flexure) andbearing members 14 in an upside-down configuration (compared totraditional coarse-fine stages). Compliant joint 16 is used to connectstage member 12 and bearing member 14 to create a low pass filteringeffect. Compliant joint 16 allows fine positioning (or small motion)even when the bearing member 14 gets ‘stuck’ due to friction, whichmitigates the nonlinear friction effect of conventional bearing member14. Since only the main stage needs to be precisely controlled, only oneactuator and one sensor is needed for the present invention. Thus, costof axially compliant bearing stage assembly 10 is significantly reduced,compared to the coarse-fine stage. In the meantime, axially compliantbearing stage assembly 10 has much better load capacity since the stagehas relatively large mass and a powerful actuator is used to directlyactuate the stage 12.

Rotary Compliant Applications

Roll-to-roll manufacturing processes, that pattern and coat electronicfunctional materials on plastic films via a roll-to-roll processingsystem 100 (see FIG. 14), are considered as low-cost and high throughputtechnologies to manufacture flexible and large-area thin filmelectronics, such as organic photovoltaics, thin film transistors,light-emitting diodes, sensors and fuel cells. In a roll-to-rollmanufacturing system 100, processes are carried out by transporting aplastic film 110 continuously from unwinder 112 to winder 114 via adrive system 115 operably coupled with the winder 114 or other portionof system 100. For this purpose, the processing roller 116 is generallycontrolled by drive system 115 to move at constant velocity (CV) whiletension of the plastic media film 110 is controlled by the unwinder 112and winder 114 and/or tension loadcell 117. Precision (i.e., trackingaccuracy) of the processing roller 116 during CV motion is crucial tothe performance of roll-to-roll system 100 because the resultingpositioning error directly affects the quality of the manufacturedproducts. For example, successive print patterns are often aligned withthe previously printed patterns on the film 110 (also known as printregistration) and tracking error of the processing roller 116 during CVmotions may cause position misalignment on the successive patterns inthe film transport direction. Therefore, registration requirement isvery tight for printed electronics—typically, on the order of a fewmicrometers.

During CV motions, tracking performance is mainly affected by two typesof disturbances. The first disturbance is position-dependent drivingtorque ripple caused by cogging forces, reluctance forces, unbalancedphase forces, phase misalignment, and current offset from a servo motor.Torque ripple occurs in a periodic manner with fundamental frequencydetermined by the pole pitch of the motor. As a result, the dominantpeak of torque ripple can be effectively suppressed using force observerand/or model-based compensation. The second disturbance is caused byfriction fluctuation as the balls of the guiding bearings roll insidethe grooves.

Although there have been a few studies on mitigating the undesirableeffects of friction fluctuations on the tracking performance of thesystem during CV motions, they have not addressed the remainingbroadband disturbances (at low-to-medium frequency) that posesignificant challenges to a conventional servo controller, hampering thetracking performance of the system.

According to the principles of the present teachings, one or more rotarycompliant joints 120, also referred to as friction isolator (FI), isemployed with processing roller 116 to provide a robust andcost-effective mechatronics approach similar to that described herein inconnection with the undesirable effects of friction on linearnanopositioning (NP) stages with mechanical bearings. The fundamentalconcept of rotary compliant joint 120 is to connect the mechanicalbearings to a processing roller 116 using a joint that is very compliantin the motion direction (i.e. rotational direction about a rotationalaxis) and less compliant in a direction orthogonal to the motiondirection, thus, effectively isolating the stage from bearing friction.It has been demonstrated that rotary compliant joint 120 significantlyreduces the settling times and quadrant glitches of roller 116 withmechanical bearings during point-to-point motions and circular motions,respectively. The present teachings describe the benefits of rotarycompliant joint 120 on mitigating the effects of friction fluctuationson the precision of continuous roll-to-roll manufacturing systems, inparticular, the processing roller 116.

Compliant Joint Rotary System

FIG. 15A illustrates a schematic of a conventional rotary system forroll-to-roll manufacturing. The processing roller 116 of inertia I_(p)is guided by a pair of rotary ball bearings 122, each of inertia I_(a),rotationally mounted or otherwise joined to a base or other structure123 to support rotational movement about a rotational axis. The viscousfriction coefficient between the sliding surfaces of the bearings 122 isdenoted as c_(f). Disturbances during constant velocity (CV) motions dueto friction fluctuations are modeled as torques T_(f1) and T_(f2); T_(a)and T_(d) are respectively the motor driving torque and othermiscellaneous disturbances such as motor torque ripple and processinduced disturbance. However, FIG. 15B illustrates a schematic of arotationally compliant bearing roller assembly 102 (also referred to ascompliant joint rotary system 102) for high precision roll-to-rollmanufacturing. Rather than being rigidly attached to the processingroller 116 (as illustrated in FIG. 15A), the inner rings of the ballbearings 122 are connected using rotary compliant joints 120 ofstiffness k and damping coefficient c. The rotary compliant joints 120provide sufficient compliance in the motion direction (i.e., θ) whileremaining stiff in other off-motion directions. Note that θ_(p), θ_(a1)and θ_(a2) are the angular positions of the processing roller 116 andtwo rotary bearings 122, respectively.

Assuming rigid body behavior, the plant dynamics (i.e., transferfunction from motor driving torque to angular position of the processingroller 116) can be derived as

$\begin{matrix}{G_{p,R} = \frac{1}{{\left( {I_{p} + {2I_{a}}} \right)s^{2}} + {2c_{f}s}}} & (1) \\{{{G_{p,{FI}} = \frac{{I_{a}s^{2}} + {\left( {c + c_{f}} \right)s} + k}{{a_{4}s^{4}} + {a_{3}s^{3}} + {a_{2}s^{2}} + {a_{1}s}}};}{{a_{4} = {I_{p}I_{a}}};{a_{3} = {{c\left( {I_{p} + {2I_{a}}} \right)} + {c_{f}I_{p}}}};}{{a_{2} = {{k\left( {I_{p} + {2I_{a}}} \right)} + {2cc_{f}}}};{a_{1} = {2kc_{f}}}}} & (2)\end{matrix}$

where s is the Laplace variable, and subscripts R and FI denote thecases without and with rotary compliant joint 120, respectively.Similarly, the open loop transfer function from frictional disturbanceto angular position of the roller 116 (assuming T_(f1)=T_(f2)) can beobtained as

$\begin{matrix}{D_{d,R} = {2G_{p,R}}} & (3) \\{D_{d,{FI}} = {2G_{p,{FI}}\frac{{cs} + k}{{I_{a}s^{2}} + {\left( {c + c_{f}} \right)s} + k}}} & (4)\end{matrix}$

Observe that in a conventional rotary system, the frictional disturbancedirectly affects the stage dynamics, jeopardizing precision of theprocessing roller 116. In the compliant joint rotary system 102, theundesirable effects of friction fluctuations are mechanically low-passfiltered through the additional dynamics introduced by the rotarycompliant joints 120. However, note that high enough c+c_(f) is neededto avoid large amplitude at the dominant resonance of the rotarycompliant joints 120. Large values of c reduce the low-pass filteringeffect at frequency regions beyond the dominant resonance due to thepresence of c in the numerator of D_(d,FI). Therefore, it is moredesirable to increase c+c_(f) by increasing c_(f).

Frequency Domain Analysis

To further illustrate the benefits of rotary compliant joint 120 inmitigating the undesirable effects of frictional disturbance, frequencydomain analysis is carried out. As illustrated in FIG. 16, an industrialstandard PID controller is used to control the motion of processingroller 116; it is tuned to 100 Hz closed loop bandwidth. Since thefeedback controller has limited ability in rejecting disturbances, aninverse-model-based disturbance observer (DOB) is implemented to furtherattenuate the low frequency disturbances due to frictional variations;it is tuned to 80 Hz bandwidth. The closed loop transfer function fromfrictional disturbance to roller position is then obtained

$\begin{matrix}{{G_{d,R} = \frac{D_{R}{G_{n}\left( {1 - Q} \right)}}{{Q\left( {G_{p,R} - G_{n}} \right)} + {G_{n}\left( {1 + {CG_{p,R}}} \right)}}}{G_{d,{FI}} = \frac{D_{FI}{G_{n}\left( {1 - Q} \right)}}{{Q\left( {G_{p,{FI}} - G_{n}} \right)} + {G_{n}\left( {1 + {CG}_{p,{FI}}} \right)}}}} & (5)\end{matrix}$

where C is the feedback (PID) controller (the derivative action islow-pass filtered using a first order filter with time constant τ), Q isa low-pass filter to guarantee the stability of the DOB, andG_(n)=G_(p,R) is the nominal plant model that describes thelow-frequency characteristics of the conventional rotary system(dominated by rigid body dynamics). They are given by

$\begin{matrix}{C = {K_{p} + \frac{K_{d}s}{{\tau s} + 1} + \frac{K_{i}}{s}}} & (6) \\{Q = \frac{\left( {2\pi\; f_{Q}} \right)^{2}}{\left( {s + {2\pi\; f_{Q}}} \right)^{2}}} & (7)\end{matrix}$

TABLE I Parameters of the Rotary System Parameters Value I_(p) 0.15 kgm²I_(a) 0.015 kgm² K_(ρ) 1.54 × 10⁴ N/rad K_(d) 81.62 Ns/rad K_(i) 6.16 ×10⁵ N/rad · s T_(f) 0.0005884 s f_(Q) 80 Hz

FIGS. 17A and 17B compare the magnitudes of G_(d,R) and G_(d,FI) usingdifferent stiffness k for rotary compliant joint 120 (FI). Note that amodal damping of 0.1% is introduced to account for the damping of therotary compliant joint 120 (i.e., c) and the remaining parameters aresummarized in Table I. Observe that the frictional disturbance in thehigh frequency region is effectively suppressed by rotary compliantjoint 120, thanks to its low-pass filtering effect. The benefits ofrotary compliant joint 120 become more dominant when the stiffness isreduced since the magnitude of G_(d,FI) rolls off after the resonancepeak. In other words, a lower stiffness rotary compliant joint 120 leadsto better mitigation of frictional disturbance. FIG. 17B shows theinfluence of viscous friction (cf) on the effectiveness of rotarycompliant joint 120. Since rotary compliant joint 120 often has limiteddamping, the resonance peak has very large amplitude if the frictionaldamping is small. This poses significant challenge since the dominantresonance can be easily excited (e.g., by friction variation),generating large position errors. Therefore, a high damping coefficientat the bearing location is necessary to attenuate the resonance peak andachieve the desired performance of rotary compliant joint 120.

Design of Rotary System 102 with Rotary Compliant Joint 120

To validate the present embodiment, a compliant joint rotary system 102is constructed as illustrated in FIGS. 18A-18B. The processing roller116, having a diameter (for example) of 160 mm, is guided by a pair ofangular contact ball bearings 122 (NSK, 7013A). A direct-drive rotary(DDR) motor 130 (Kollmorgen, C042A) is used to drive the system. Rotarycompliant joints 120, according to the principles of the presentteachings, are used to connect the processing roller 116 to the innerrings of the bearings 122. A rotary eddy current mechanism 132 isimplemented to achieve the desired viscous damping at the bearinglocation, as discussed in the next section.

Design of Rotary Compliant Joint 120

As illustrated in FIGS. 19A-19B, in some embodiments, a symmetriccartwheel flexure (SCF) mechanism 134 with four flexure leaf springs 136is adopted for rotary compliant joint 120; the center platform 138 ofthe SCF mechanism 134 is connected to the processing roller 116 and theouter platform 140 is connected to the inner ring of the ball bearing122. The symmetric structure of SCF mechanism 134 reduces drift of therotation center during motion. In addition, the over-constrained flexuremechanism effectively improves rigidity in off-motion directions.

To achieve the desired attenuation of frictional disturbance, the rotarycompliant joint 120 should have minimal stiffness in the motiondirection (i.e., θ_(z)). In the meantime, it must maintain highstiffness in the off-motion directions (e.g., radial directions), so asnot to overly sacrifice the rigidity of the ball bearing. Therefore, theparameters of the SCF mechanism 134, specifically, leaf length l, leafthickness t, leaf width b, and outer platform radius r are optimized tomaximize the stiffness ratios between off-motion directions and motiondirection while satisfying other design constraints (e.g., maximumstress and dimension). Let us denote K₁₁-K₆₆ as the stiffness of the SCFmechanism 134 in the x, y, z, θ_(x), θ_(y) and θ_(z), directions; theobjective can then be expressed asMaximize K ₁₁ /K ₆₆ where I=1, . . . ,5  (8)

There are several constraints regarding the stiffness, stress anddimension limitations of the flexure mechanism. First of all, the axialand radial stiffness of the SCF should be of similar order of magnitudeas the ball bearings so as not to overly sacrifice the rigidity of thesystem. Therefore, for purposes of illustration and not intending to belimiting on the present teachings, the following constraints areimprosed to fulfill the stiffness requirement in an exemplaryconfiguration based on the approximated off-motion stiffness of ballbearings from the manufacturer's (e.g., NSK) catalogK ₁₁ ,K ₂₂ and K ₃₃≥120 N/μm  (9)

Secondly, certain dimensional limitations are imposed on this 22xemplarydesign of SCF since to fit into an exemplary designed rotary system:30 mm≤r ₁ <r≤60 mm (where r ₁ =r−1)  (10)0<b≤30 mm  (11)0.5 mm≤t≤I/10  (12)

Eq. (10) indicates that the center 138 and outer 140 platforms of SCFmechanism 134 should have large enough radius to prevent excessivedeformation under loading. Note that the overall radius of theprocessing roller 116 in this example is set to 80 mm such that a samplelength of 500 mm can be processed by a single turn. Furthermore, in Eq.(11), the width of the SCF mechanism 134 is constrained to limit theoverall length of the drive shaft and prevent low torsional stiffness.Finally, the thickness of the flexure leaf springs 136 is constrained toavoid manufacturing issues while maintaining thin beam assumption.

To facilitate the design optimization, the stiffness of SCF mechanism134 is derived analytically. Note that the nonlinear stiffening effectof the over-constrained flexure is ignored in this model for simplicityand the off-diagonal terms in the stiffness matrix become zero as aresult of the symmetric structure of the SCF mechanism 134. Theremaining diagonal terms are given by

$\begin{matrix}{K_{11} = {K_{22} \approx {2{\alpha\beta}\;{El}}}} & (13) \\{K_{33} \approx \frac{4\alpha\beta^{3}El}{B}} & (14) \\{K_{44} = {K_{55} \approx {\frac{\alpha\beta^{3}El^{3}}{6}\left( {1 + \frac{{2\xi} - 1}{B}} \right)}}} & (15) \\{K_{66} \approx \frac{2\alpha^{3}\beta\xi El^{3}}{3}} & (16)\end{matrix}$

where E is the Young's modulus, u is the Poisson's ratio and thenon-dimensional parameters are described as follows

$\begin{matrix}{{{\alpha = \frac{t}{l}};{\beta = \frac{b}{l}};{\gamma = \frac{r}{l}};{\gamma_{i} = \frac{r_{i}}{l}};}{{\xi = {{2 + {6{\gamma\left( {\gamma - 1} \right)}}} = {2 + {6{\gamma_{i}\left( {\gamma_{i} + 1} \right)}}}}};}{B = {1 + \frac{12{\beta^{2}\left( {1 + \upsilon} \right)}}{5}}}} & (17)\end{matrix}$

The stiffness ratios of off-motion directions over motion direction canthen be calculated as

$\begin{matrix}{\frac{K_{11}}{K_{66}} = {\frac{K_{22}}{K_{66}} \approx \frac{3}{\alpha^{2}l^{2}\xi}}} & (18) \\{\frac{K_{33}}{K_{66}} \approx \frac{6\beta^{2}}{\alpha^{2}l^{2}\xi B}} & (19) \\{\frac{K_{44}}{K_{66}} = {\frac{K_{55}}{K_{66}} \approx {\frac{\beta^{2}}{4\alpha^{2}\xi}\left( {1 + \frac{{2\xi} - 1}{B}} \right)}}} & (20)\end{matrix}$

Before stepping into detailed optimization, sensitivity analysis iscarried out to illustrate the effects of different design parameters onthe objective. Observe from Eq. (13)-(16) and (18)-(20) that increasingβ always leads to higher off-motion stiffness as well as higherstiffness ratios between K₃₃-K₅₅ and K₆₆. This indicates that should beset to its upper limit. Therefore, b=30 mm is used to achieve thelargest possible β given a fixed l. Similarly, as ξ decreases, thestiffness ratios are increased without affecting the off-motionstiffness K₁₁-K₃₃. Since monotonically increases for γ_(i) (or r_(i))>0,r_(i) is set to its lower limit of 30 mm to minimize ξ. As a result, thedesign problem is simplified to find the optimal parameters for l and α.

FIG. 20 illustrates the calculated stiffness ratio of K₁₁ (and K₂₂) overK₆₆ as a function of α and l. Observe that reducing a leadsmonotonically increased stiffness ratio at a fixed l. Therefore, tshould be set to its lower limit of 0.5 mm to achieve a minimum a.Although a larger l generally enables the choice of a lower α, thus,higher stiffness ratio, it cannot be arbitrary increased due to theexistence of other design constraints. By plotting the active geometryand stiffness constraints from Eq. (9)-(12), the stiffness ratio of K₁₁(and K₂₂) over K₆₆ is maximized at a leaf length (l) of 26 mm(highlighted by the red circle in FIG. 8). Similar behavior is observedfor other stiffness ratios and exactly the same optimal parameters areobtained for α and l—see Table II.

TABLE II Optimal Parameters of Designed FI in Exemplary ConfigurationParameters Value l 26 mm b 30 mm t 0.5 mm  r 56 mm

Briefly, in some embodiments, rotary eddy current mechanism 132, thepermanent magnets can be arranged in a circumferential direction, whichis similar to that of a doubled-sided linear motor. A rotating disc canbe placed between the upper and lower magnetic arrays and viscousdamping torque can be achieved due to the interaction of eddy currentand magnetic field. In some embodiments, the eddy current mechanism 132is configured to provide negative stiffness in the rotational direction.In some embodiments, the eddy current mechanism 132 is configured toprovide rotational damping.

Experimental Validation of Rotary Compliant Joint System

As part of experimental validation of the compliant joint rotary system102 and rotary compliant joint 120, rotary system 102 was constructed inaccordance with the present teachings. It was determined that theintroduction of rotary compliant joint 120 greatly attenuates thefrictional disturbance with frequency components above its dominantresonance, making it much easier for a disturbance observer (DOB) of thesame bandwidth to suppress the remaining low frequency disturbance. As aresult, the tracking error of the compliant joint rotary system 102 athigh-speed motion was significantly smaller than that of the casewithout rotary compliant joint 120. In addition, the introduction ofrotary compliant joint 120 enabled the use of a DOB with much higherbandwidth, leading to up to 61% reduction in RMS error when compared tothe case without rotary compliant joint 120. The tracking performance ofthe friction-isolated system also remains largely unchanged as the speedof the processing roller 116 varies, indicating that the presentteachings are very robust.

CONCLUSION

According to the present teachings, a novel rotary servo system forachieving high precision continuous roll-to-roll manufacturing has beenprovided. The present system integrates a rotary compliant joint 120(friction isolator (FI)), a mechanical component, to mitigate theundesirable effects of friction on the tracking performance of theprocessing roller 116 during constant velocity motions, thus improvingthe quality of the manufactured products. It has been demonstratedthrough frequency domain analysis that rotary compliant joint 120improves the disturbance rejection ability of the system by low-passfiltering the frictional disturbance of the supporting bearings. It hasbeen demonstrated in experiments that the compliant joint rotary systemachieves up to 61% reductions in RMS tracking error during CV motions ofdifferent speed, compared to a conventional rotary system.

The foregoing description of the embodiments has been provided forpurposes of illustration and description. It is not intended to beexhaustive or to limit the disclosure. Individual elements or featuresof a particular embodiment are generally not limited to that particularembodiment, but, where applicable, are interchangeable and can be usedin a selected embodiment, even if not specifically shown or described.The same may also be varied in many ways. Such variations are not to beregarded as a departure from the disclosure, and all such modificationsare intended to be included within the scope of the disclosure.

What is claimed is:
 1. A rotationally compliant bearing roller assemblycomprising: a roller; at least one bearing member operably coupled to abase configured to support rotational movement about a rotational axis;and a rotary compliant joint interconnecting the at least one bearingmember to the roller, the rotary compliant joint having a firstcompliance in a rotational direction about the rotational axis to permitmovement of the roller in the rotational direction relative to the atleast one bearing member, the rotary compliant joint having a secondcompliance in a direction orthogonal to the rotational direction, thesecond compliance being less than the first compliance.
 2. Therotationally compliant bearing roller assembly according to claim 1further comprising: actuating drive system configured to cause theroller to rotate about the rotational axis in the rotational direction.3. The rotationally compliant bearing roller assembly according to claim1 further comprising: actuating drive system configured to move a mediafilm over the roller thereby causing the roller to rotate about therotational axis in the rotational direction.
 4. The rotationallycompliant bearing roller assembly according to claim 1 furthercomprising: a sensor for measuring motion of the roller.
 5. Therotationally compliant bearing roller assembly according to claim 1wherein the rotary compliant joint comprises a flexure mechanism.
 6. Therotationally compliant bearing roller assembly according to claim 5wherein the flexure mechanism comprises a first member coupled to the atleast one bearing member, a second member coupled to the roller, and oneor more compliant members interconnecting the first member and thesecond member.
 7. The rotationally compliant bearing roller assemblyaccording to claim 6 wherein the one or more compliant members comprisesa plurality of leaf springs coupled between the first and second member.8. The rotationally compliant bearing roller assembly according to claim7 wherein each of the plurality of leaf springs provides compliantmovement in the rotational direction and inhibits compliant movement indirections perpendicular to the rotational directions.
 9. Therotationally compliant bearing roller assembly according to claim 5wherein the flexure mechanism provides positive stiffness in therotational direction and negative stiffness in the rotational direction.10. The rotationally compliant bearing roller assembly according toclaim 5 wherein the stiffness of the flexure mechanism in directionsperpendicular to the rotational direction has greater magnitude than thestiffness of the flexure mechanism in the rotational direction.
 11. Therotationally compliant bearing roller assembly according to claim 5wherein an engage and disengage mechanism is applied to the flexuremechanism between the roller and the at least one bearing member. 12.The rotationally compliant bearing roller assembly according to claim 1wherein the at least one bearing member comprising a pair of bearingmembers slidably operably coupled to the base configured to support therotational movement of the roller about the rotational axis.
 13. Therotationally compliant bearing roller assembly according to claim 1wherein the combined stiffness of the rotary compliant joint and the atleast one bearing member in a first direction perpendicular to therotational direction and a second direction perpendicular to therotational direction has the same order of magnitude as the stiffness ofthe at least one bearing member alone in the first direction and thesecond direction.
 14. The rotationally compliant bearing roller assemblyaccording to claim 1 wherein a damper is coupled to the rotary compliantjoint to increase the damping coefficient in the rotational direction.15. The rotationally compliant bearing roller assembly according toclaim 1 wherein a control system provides active damping control signalthrough the drive system of the roller to increase the damping betweenthe roller and the at least one bearing member.
 16. The rotationallycompliant bearing roller assembly according to claim 1 wherein therotary compliant joint comprises an eddy current mechanism.
 17. Therotationally compliant bearing roller assembly according to claim 16wherein the eddy current mechanism is configured to provide negativestiffness in the rotational direction.
 18. The rotationally compliantbearing roller assembly according to claim 16 wherein the eddy currentmechanism is configured to provide rotational damping.